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Existing phase optimization methods in reconfigurable intelligent surfaces (RISs) face significant challenges in achieving flexible beam synthesis, especially for directional beam suppression. This paper introduces a Max-min criterion incorporating non-linear constraints, utilizing optimization techniques to enable multi-beam enhancement and suppression via transmissive RISs. A realistic model grounded in geometrical optics is first presented to characterize the input/output behavior of transmissive RIS, effectively linking explicit beam-forming operations with practical implementation. Subsequently, a highly efficient bisection-based algorithm for constrained Max-min optimization involving quadratic forms is developed, utilizing an auxiliary variable and Moreau envelope to iteratively reach the optimal solution. This approach demonstrates excellent extensibility and is applicable to a wide range of constrained Max-min problems. Numerical simulations validate the proposed methods, confirming that the framework enables beam enhancement or suppression at designated spatial positions.

As an emerging wireless communication technology, reconfigurable intelligent surface (RIS) has become a basic choice for providing signal coverage services in scenarios with dense obstacles or long tunnels through multi-hop configurations. Conventional works of literature mainly focus on alternating optimization or single-beam calculation in RIS phase configuration, which is limited in considering energy efficiency, and often suffers from inaccurate channel state information (CSI), poor convergence, and high computational complexity. This paper addresses the design and optimization challenges for successive RIS-assisted multi-hop systems. Specifically, we establish a general model for multi-hop communication based on the relationship between the input and output electric fields within each RIS. Meanwhile, we derive the half-power beamwidth of the RIS-reflected beams, considering the beam direction. Leveraging these models and derivations, we propose deployment optimization and beam optimization strategies for multi-hop systems, which feature high aperture efficiency and significant gains in signal power. Simulation and prototype experiment results validate the effectiveness and superiority of the proposed systems and methods.

The existing methods for Reconfigurable Intelligent Surface (RIS) beamforming in wireless communication are typically limited to uniform phase quantization. However, in real world applications, the phase and bit resolution of RIS units are often non-uniform due to practical requirements and engineering challenges. To fill this research gap, we formulate an optimization problem for discrete non-uniform phase configuration in RIS assisted multiple-input single-output (MISO) communications. Subsequently, a partition-and-traversal (PAT) algorithm is proposed to solve that, achieving the global optimal solution. The efficacy and superiority of the PAT algorithm are validated through numerical simulations, and the impact of non-uniform phase quantization on system performance is analyzed.

This paper investigates a general discrete $\ell_p$-norm maximization problem, with the power enhancement at steering directions through reconfigurable intelligent surfaces (RISs) as an instance. We propose a mathematically concise iterative framework composed of alternating inner product maximizations, well-suited for addressing $\ell_1$- and $\ell_2$-norm maximizations with either discrete or continuous uni-modular variable constraints. The iteration is proven to be monotonically non-decreasing. Moreover, this framework exhibits a distinctive capability to mitigate performance degradation due to discrete quantization, establishing it as the first post-rounding lifting approach applicable to any algorithm intended for the continuous solution. Additionally, as an integral component of the alternating iterations framework, we present a divide-and-sort (DaS) method to tackle the discrete inner product maximization problem. In the realm of $\ell_\infty$-norm maximization with discrete uni-modular constraints, the DaS ensures the identification of the global optimum with polynomial search complexity. We validate the effectiveness of the alternating inner product maximization framework in beamforming through RISs using both numerical experiments and field trials on prototypes. The results demonstrate that the proposed approach achieves higher power enhancement and outperforms other competitors. Finally, we show that discrete phase configurations with moderate quantization bits (e.g., 4-bit) exhibit comparable performance to continuous configurations in terms of power gains.

The conventional beam management procedure mandates that the user equipment (UE) periodically measure the received signal reference power (RSRP) and transmit these measurements to the base station (BS). The challenge lies in balancing the number of beams used: it should be large enough to identify high-RSRP beams but small enough to minimize reporting overhead. This paper investigates this essential performance-versus-overhead trade-off using Bayesian optimization. The proposed approach represents the first application of real-time beam tracking via Bayesian optimization in RIS-assisted communication systems. Simulation results validate the effectiveness of this scheme.

A fair beam allocation framework through reconfigurable intelligent surfaces (RISs) is proposed, incorporating the Max-min criterion. This framework focuses on designing explicit beamforming functionalities through optimization. Firstly, realistic models, grounded in geometrical optics, are introduced to characterize the input/output behaviors of RISs, effectively bridging the gap between the requirements on explicit beamforming operations and their practical implementations. Then, a highly efficient algorithm is developed for Max-min optimizations involving quadratic forms. Leveraging the Moreau-Yosida approximation, we successfully reformulate the original problem and propose iterations to attain the optimal solution. A comprehensive analysis of the algorithm's convergence is provided. Importantly, this approach exhibits excellent extensibility, making it readily applicable to address a broader class of Max-min optimization problems. Finally, numerical and prototype experiments are conducted to validate the effectiveness of the framework. With the proposed beam allocation framework and algorithm, we clarify that several crucial redistribution functionalities of RISs, such as explicit beam-splitting, fair beam allocation, and wide-beam generation, can be effectively implemented. These explicit beamforming functionalities have not been thoroughly examined previously.

This paper addresses the hardware structure of Reconfigurable Intelligent Surfaces (RIS) and presents a comprehensive overview of RIS design, considering both unit design and prototype systems. It commences by tracing the evolutionary trajectory of RIS, originating from static cell-structured hypersurfaces. The article conducts a meticulous examination from the standpoint of adaptability, elucidating the diverse array of unit structures and design philosophies that underlie existing RIS frameworks. Following this, the study systematically categorizes and synthesizes channel modeling research for RIS-facilitated wireless communication, leveraging both physical insights and statistical data. Additionally, the article provides a detailed exposition of current RIS experimental setups and their corresponding empirical findings, delving into the attributes of prototype design and system functionalities. Moreover, this work introduces an in-house developed RIS prototype. The prototype undergoes rigorous empirical evaluation, encompassing multi-hop RIS signal amplification, image reconstruction, and real-world indoor signal coverage experiments. The empirical results robustly affirm the efficacy of RIS in effectively mitigating signal coverage blind spots and enabling radio wave imaging. With RIS-enhanced augmentation, the average indoor signal gain surpasses 8 dB.